Numerical inverse scattering for the Korteweg–-de Vries and modified Korteweg–-de Vries equations

Recent advances in the numerical solution of Riemann–Hilbert problems allow for the implementation of a Cauchy initial value problem solver for the Korteweg–de Vries equation (KdV) and the defocusing modified Korteweg–de Vries equation (mKdV), without any boundary approximation. Borrowing ideas from the method of nonlinear steepest descent, this method is demonstrated to be asymptotically accurate. The method is straightforward for the case of defocusing mKdV due to the lack of poles in the Riemann–Hilbert problem and the boundedness properties of the reflection coefficient. Solving KdV requires the introduction of poles in the Riemann–Hilbert problem and more complicated deformations. The introduction of a new deformation for KdV allows for the stable asymptotic computation of the solution in the entire (x, t)-plane. KdV and mKdV are dispersive equations and this method can fully capture the dispersion with spectral accuracy. Thus, this method can be used as a benchmarking tool for determining the effectiveness of future numerical methods designed to capture dispersion. This method can easily be adapted to other integrable equations with Riemann–Hilbert formulations, such as the nonlinear Schrödinger equation

Re-escribiendo a Heidegger

Two traps currently ensnare Heideggerian scholarship: the “language trap” and the “being trap.” To avoid them, the text argues we should follow Heidegger’s important indication that movement (aka ex-sistential becoming or Zeit) determines all forms of meaning (aka the significance of things or Sein). This requires a radical rewriting of the terminology and the structure of Zeitlichkeit in § 65 of Sein und Zeit. The text also argues for moving beyond Heidegger’s early and late formulations of fundamental ontology and into a metaontological ethics that would apply to the economic, social, and political worlds in which we live our daily lives.Dos trampas atrapan actualmente a la erudición heideggeriana: la “trampa del lenguaje” y la “trampa del ser.” Para evitarlas, el texto argumenta que deberíamos seguir la importante indicación de Heidegger de que el movimiento (entendido como devenir ex-sistencial o Zeit) determina todas las formas de significado (entendidas como la significación de las cosas o Sein). Esto requiere una reescritura radical de la terminología y la estructura de Zeitlichkeit en el § 65 de Sein und Zeit. El texto también aboga por ir más allá de las formulaciones tempranas y tardías de Heidegger sobre la ontología fundamental y adentrarse en una ética metaontológica que se aplicaría a los mundos económico, social y político en los que vivimos nuestra vida cotidiana

Book Review: Richard Kearney and Jens Zimmerman, eds., Reimagining the Sacred: Richard Kearney Debates God (New York: Columbia University Press, 2015), viii + 286 pages.

A book review of Richard Kearney and Jens Zimmerman, eds., Reimagining the Sacred: Richard Kearney Debates God (New York: Columbia University Press, 2015)

The value of contractual terms in office leases

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (leaf 41).This paper uses a comprehensive data set to develop a hedonic model of office rent that estimates values of contractual terms such as tenant improvement allowances, leasing commissions, and options. The model includes variables to control for building characteristics and market conditions, as well as basic lease terms. Although other studies have used a similar approach, the prior work in this area was limited by the lack of data regarding contractual terms. The results show that there is a consistent, upward-sloping, convex term structure of rent. Furthermore, there is an insignificant "size premium" but the "proportion discount" is significant. In general, other variables, such as location variables and qualitative variables behave as expected, with the exception of the expense type dummy variables. Tenant improvement allowances and leasing commissions paid by the landlord do not have a predictable impact on rent at low levels. But high levels of allowances and commissions result in significant rent premiums. These results indicate that lower levels of allowances and commissions may be expected by the market. At higher levels, however, these contractual terms are clearly priced into rent levels.(cont.) Renewal options appear to have positive impacts in some years and negative impacts in other years. Renewal options may represent amenities that are granted to tenants as inducements in weaker leasing markets but are priced in stronger markets. Termination options and rights of first offer/refusal appear to have negative impacts on rent that are somewhat consistent in all years. This is counterintuitive because these options are thought to benefit the tenant. One explanation is that these options are in fact beneficial to the landlord. Further study is necessary to understand the value of these options. Overall, more information about options terms would be beneficial. Information such as the renewal rent, the termination fee, and the size of the offer/refusal space would help us to understand the economic arrangement between the parties and to predict the corresponding impact on rent.by Kevin T. Sheehan.S.M